MR2075293
Futoshi TAKAHASHI
Futoshi TAKAHASHI
On the Location of Blow up Points of Least Energy Solutions to the Brezis-Nirenberg Equation
Funkcialaj Ekvacioj. Serio Internacia
47
2004
145--166
http://fe.math.kobe-u.ac.jp/FE/FullPapers/47-1/47_145.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2075293
In this paper, we study the asymptotic behavior of solutions to the semilinear elliptic problem involving critical Sobolev exponent with lower order perturbation, which was considered by Han and Rey before. We focus our attention on the least energy solutions obtained by the method of Brezis and Nirenberg, and show that the blow up point of the least energy solutions is a minimum point of the (positive) Robin function on the domain. This additional characterization extends the former result of Han and Rey in this case.
Least energy solutions, Critical Sobolev exponent, Robin function, Blow up point.
Primary 35B40; Secondary 35J20.
47-167
2004
On the Location of Blow up Points of Least Energy Solutions to the Brezis-Nirenberg Equation
Futoshi TAKAHASHI
Futoshi TAKAHASHI
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